Claus Beisbart

The voting power of a voter—the extent to which she can affect the outcome of a collective decision—is often quantified in terms of the probability that she is critical. This measure is extended to a series of power measures of different ranks. The measures quantify the extent to which a voter can be part of a group that can jointly make a difference as to whether a bill passes or not. It is argued that the series of these measures allow for a more appropriate assessment of voting power, particularly of a posteriori voting power in case the votes are stochastically dependent. Also, the new measures discriminate between voting games that cannot be distinguished in terms of the probability of only criticality.

We provide welfarist evaluations of decision rules for federations of states and consider models, under which the interests of people from different states are stochastically dependent. We concentrate on two welfarist standards; they require that the expected utility for the federation be maximized or that the expected utilities for people from different states be equal. We discuss an analytic result that characterizes the decision rule with maximum expected utility, set up a class of models that display interstate dependencies and run simulations for different dependency scenarios in the European Union. We find that, under positive correlations, the welfare distribution tends to be less sensitive to the choice of the decision rule, whereas it can be important under negative correlations. The results that Beisbart and Bovens (SCW 29, p. 581, 2007) have found for two types of models without interstate dependencies are relatively stable. There are exceptions, though, under which the way the welfare distribution is shaped by a decision rule is significantly affected by dependencies.

N. Bostrom’s simulation argument and two additional assumptions imply that we likely live in a computer simulation. The argument is based upon the following assumption about the workings of realistic brain simulations: The hardware of a computer on which a brain simulation is run bears a close analogy to the brain itself. To inquire whether this is so, I analyze how computer simulations trace processes in their targets. I describe simulations as fictional, mathematical, pictorial, and material models. Even though the computer hardware does provide a material model of the target, this does not suffice to underwrite the simulation argument because the ways in which parts of the computer hardware interact during simulations do not resemble the ways in which neurons interact in the brain. Further, there are computer simulations of all kinds of systems, and it would be unreasonable to infer that some computers display consciousness just because they simulate brains rather than, say, galaxies.

The choice of a social decision rule for a federal assembly affects the welfare distribution within the federation. But which decision rules can be recommended on welfarist grounds? In this paper, we focus on two welfarist desiderata, viz. (i) maximizing the expected utility of the whole federation and (ii) equalizing the expected utilities of people from different states in the federation. We consider the European Union as an example, set up a probabilistic model of decision making and explore how different decision rules fare with regard to the desiderata. We start with a default model, where the interests, and therefore the votes of the different states are not correlated. This default model is then abandoned in favor of models with correlations. We perform computer simulations and find that decision rules with a low acceptance threshold do generally better in terms of desideratum (i), whereas the rules presented in the Accession Treaty and in the (still unratified) Constitution of the European Union tend to do better in terms of desideratum (ii). The ranking obtained regarding desideratum (i) is fairly stable across different correlation patterns.

How can probabilistic models from physics represent a target, and how can one understand the probabilities that figure in such models? The aim of this chapter is to answer these questions by analyzing random models of Brownian motion and point process models of the galaxy distribution as examples. This chapter defends the view that such models represent because we may learn from them by setting our degrees of belief following the probabilities suggested by the model. This account is not incompatible with an objectivist view of the pertinent probabilities, but stock objectivist interpretations, e.g., frequentism or Lewis’ Humean account of probabilities have problems to provide a suitable objectivist methodology for statistical inference from data. This point is made by contrasting Bayesian statistics with error statistics.

Statistical physicists assume a probability distribution over micro-states to explain thermodynamic behavior. The question of this paper is whether these probabilities are part of a best system and can thus be interpreted as Humean chances. I consider two Boltzmannian accounts of the Second Law, viz. a globalist and a localist one. In both cases, the probabilities fail to be chances because they have rivals that are roughly equally good. I conclude with the diagnosis that well-defined micro-probabilities under-estimate the robust character of explanations in statistical physics.